1. Technical Field
The present invention relates to a wiener_filter used for a reduction in a noise of data (i.e., for an improvement in a signal to noise ratio (SNR)) and data processing. In particular, the present invention relates to a data processing system, a data processing method, a diagnostic imaging apparatus, and a magnetic resonance imaging apparatus for optimally processing data depending on the noise of data and deterioration characteristics.
2. Related Art
A magnetic resonance imaging is a technique for magnetically exciting nuclear spins in a patient (subject) located in a static magnetic field by using a high Larmor frequency and reconstructing an image from MR signals, such as echo signals, generated in response to the excitation. For the magnetic resonance imaging, it is very important to improve the SNR and spatial resolution per unit time.
A wiener_filter (WF) that was devised based on likelihood maximization of the amount of information is available. The WF is a filter for optimizing the SNR of data defined in Fourier space (also referred to as “k space” or “frequency space”). In theory, an ideal_WF is defined in Fourier space and a WF aimed for only noise recovery processing (the WF will be particularly referred to as a wiener-smoothing-filter (WSF)) is represented as a following expression (1), where “Ps” indicates signal power (power spectrum) and “Pn” indicates noise power.
                    WF        =                  Ps                      Ps            +            Pn                                              (        1        )            
Alternatively, if the SNR is defined as a following expression (2), the WF is represented as a following expression (3) from the expressions (1) and (2).
                    SNR        =                  Ps          Pn                                    (        2        )                                WF        =                  1                                                            ⁢                          1              ⁢                                                          +                                                          ⁢                              1                                                                                          ⁢                  SNR                                                                                        (        3        )            
The expression (3) is defined based on a variety of assumptions and a particularly important point is that the Ps must be the signal power that does not contain the noise. In addition, a general expression including not only the noise but also recovery processing of deterioration, such as blur, is represented as a following expression (4), where “H” indicates a deterioration characteristic in the filter space and “*” indicates a complex conjugate.
                    WF        =                              H            *            Ps                                                                                                  H                                                  2                            ⁢              Ps                        +            Pn                                              (        4        )            
However, in the actual application of the WF, when the H and the Pn are known or measurable, the values are used as the H and the Pn. On the other hand, since an ideal signal power (ideal_Ps) that does not contain the noise cannot be generally known, the ideal_Ps cannot be used as the Ps. Accordingly, actual data is first measured and noise-contaminated signal power (Psd) is used as the ideal_Ps to determine the WF in an approximated manner.
In addition, although the WF was originally conceived for Fourier space, it is not only applied to frequency space, but is also applied to, for example, fresnel transform band splitting (FREBAS) space, in which the deterioration of high frequency components is considered to be less.
However, compared to a case in which the ideal_Ps is used, the related art is greatly inferior in performance for an improvement in the SNR, i.e., a reduction in the noise while maintaining a spatial frequency. In addition, for data having a smaller SNR, the deterioration of the image quality (filtering effect) is more prominent. Thus, when the WF is actually used, the issue is how to estimate the ideal_Ps based on the Psd, which is a noise-containing processing-target data.
FIG. 37 shows a gain characteristic relative to an SNR in the ideal_WF. For a portion where the SNR (=Ps/Pn) is large, i.e., where “Ps>>Pn” is sufficiently satisfied, the WF is substantially equal to 1, which does not cause a large influence. On the other hand, for a portion where the Ps approaches the Pn, the WF approaches “0” to reduce the gain, so that the noise is optimally reduced in accordance with the sizes of the Ps and the Pn while high-frequency components are reserved as much as possible.
Therefore, as shown in FIG. 38 (for the Psd with only one scan), the Ps is closer to the Pn since the gain decreases for high-frequency components of data. Thus, with the WF, variations in high-frequency components are more likely to affect the characteristics than low-frequency components.